There are two situations if the "face" is of person other than the speaker


1) in somebody's face

(North American English, informal) annoying somebody by criticizing them or telling them what to do all the time

In this context correct sentence will be as follows:
He spoke these words in his face.



2) to somebody's face
if you say something to somebody's face, you say it to them directly rather than to other people
He's a liar, and I've told him so to his face many times.

In this context correct sentence will be as follows:
He spoke these words to his face.


http://oald8.oxfordlearnersdictionar...ictionary/face


Third situation:

Face used as expressive tool:

If "his" refers to he himself then "face" also pertains to him. In that context "face" is used as symbolic expression just like:

spoke with her eyes (To be expressive).

In that context correct sentence will be as under:

He spoke these words with his face.

http://www.thefreedictionary.com/speak

These were the three proximate possibilities out of which first two are more rational choices.

On the other hand, "Upon", "on", "by" don't fit in the situation.

__________________
"Tumhary nafs ki qeemat Janat hay isy Janat say kam qeemat pey na bechna."
"Jiyo to istarh ky log tum sy milny ko tarsy; maro to istrah k log tumharee mot par royain"